Course overview
The first aim of this course is to construct Lebesgue measure on the real line, and from there construct the Lebesgue integral. These provide the basis for many of the functions studied in mathematics and physics. The second aim of the course is to develop the abstract theory of measure and integration, which has applications, among other, to probability.
- Lebesgue measure
- Integration
- L^p-spaces
Course learning outcomes
- Demonstrate proficiency in working with the Lebesgue integral
- Prove basic results about integration on the line and in abstract settings
- Demonstrate proficiency in working with spaces of integrable functions
- Construct rigorous mathematical arguments at the appropriate level
- Communicate results clearly.